The US boss in Iraq declared his forces wanted to kill or capture the former Iraqi president and the coalition would continue to scour the countryside for the fugitive leader, with a $25m price on his head.
Bremer reiterated the US would bring Saddam Hussein to justice, but played down reports that the toppled strongman was behind the resistance plaguing the US forces and Iraqis.
He also pledged that the US-led coalition would speed up the handover of political and security powers to Iraqis after a recent upswing in car bombings and other attacks.
"We believe that Saddam is alive, is in Iraq, and his capture or his killing is our top priority," Bremer told reporters. "We still have no clear indication if Saddam himself is behind these attacks."
Bremer also vowed the coalition would stand firm and not abandon Iraq in the face of the mounting violence against civilians and the rising number of US soldiers killed in action.
"We will seek ways to accelerate the transfer of authority to the government of Iraq," Bremer said on Saturday at his first media conference in Baghdad since a bombing spree claimed the lives of 43 people and wounded more than 200 last Monday.
"The coalition is still going to turn sovereignty to the Iraqi people as quickly as practicable," he said.
US officials and the UN Security Council have called on the country's interim Governing Council to set a timeframe by mid-December for the drafting of a constitution and the holding of national elections, clearing the way for Iraqi sovereignty.
Bremer aims to have the country's 50,000-strong police force reach 75,000 and the new Iraqi army, now consisting of only one battalion, reach 40,000 men by next September.
The Iraqi border police should reach 25,000. The civil defence forces, now at about 7800, should reach about 25,000, while the 20,000-strong Facilities Protection Services, which guards civilian installations and infrastructure, should climb to about 30,000, coalition officials said.
Meanwhile police said an Iraqi was killed and another wounded when a bomb they were attempting to plant on the side of a road north of Baghdad exploded.
A police commander said the men were carrying an "explosive charge" which they wanted to plant on the side of the road in the region of Taji.
He said the men realised the charge would go off before they had time to plant it so they tried to get rid of the bomb by throwing it out of their car, but the charge exploded and destroyed the vehicle.